Distributed Parameter Optimum Control of a Nuclear Rocket With Thermal Stress Constraints

1967 ◽  
Vol 89 (2) ◽  
pp. 300-306 ◽  
Author(s):  
D. L. Briggs ◽  
C. N. Shen
Keyword(s):  
Optimal Control ◽  
Thermal Stress ◽  
Flow Rate ◽  
Thermal Stresses ◽  
Control Level ◽  
Control Program ◽  
Bilinear System ◽  
Stress Constraints ◽  
Stress Constraint ◽  
Nuclear Rocket

The problem considered here is that of controlling the flow rate through a nuclear rocket such that temperature gradients in the fuel elements, and the corresponding thermal stresses produced, do not exceed specified values. The desired control program is that which takes the system from steady-state conditions at a given flow rate to a higher, specified flow rate in minimum time without violating the thermal stress constraints. The system equations here are a pair of coupled, first-order, bilinear, partial differential equations and the thermal stress constraint is proportional to a product of state and control variables. By analyzing both the solution for a step in control and the coupling between control level and time response in the bilinear system, the form of the optimal control is deduced. It is shown how the optimal control law can be generated using a digital computer. Numerical results are given.

Study of Controllability of Bilinear Systems with Limited Control

2021 ◽  
Vol 26 (3-4) ◽  
pp. 302-313
Author(s):  
L.G. Gagarina ◽  
◽  
A.A. Doronina ◽  
R.A. Fomin ◽  
D.A. Chukhlyaev ◽  
...  
Keyword(s):  
Optimal Control ◽  
Control System ◽  
Control Systems ◽  
Control Program ◽  
Bilinear System ◽  
Equation System ◽  
Bilinear Systems ◽  
Complete Controllability ◽  
Complex Objects ◽  
Bilinear Control

Optimal control is closely related to the choice of the most advantageous control modes for complex objects, which are described using ordinary differential systems. The problem of optimal control consists in calculating the optimal control program and synthesizing the optimal control system. This problem arises in the applied field of the optimal control theory, in the case when control is based on the principle of feedback and in automatic control systems. Optimal control problems, as a rule, are calculated by numerical methods to find the extremum of a functional or to solve a boundary value problem for a differential equation system. From a mathematical standpoint, the synthesis of optimal control systems is a nonlinear programming problem in functional spaces. In this study the problem of complete controllability of a bilinear control system on the plane was considered. The controllability of bilinear systems with both unlimited and limited control was studied. The evidences of closed trajectory systems controllability theorems were produced. The authors have defined multiple criteria of complete controllability for bilinear system with limited control. The complete controllability conditions of bilinear control system have been proposed with their algebraic reasoning. In the contemporary context of universal robotization of production, completely controllable systems matter in navigation, as well as in modeling of a number of economic and social processes.

Switching Analysis for Constrained Bilinear Distributed Parameter System With Applications

1969 ◽  
Vol 91 (2) ◽  
pp. 277-283 ◽  
Author(s):  
D. L. Briggs ◽  
C. N. Shen
Keyword(s):  
Optimal Control ◽  
Boundary Control ◽  
Initial Conditions ◽  
Control Program ◽  
Necessary Condition ◽  
Stress Constraint ◽  
Distributed Parameter ◽  
Distributed Parameter System ◽  
Parameter System ◽  
State Equations

A distributed parameter thermal and stress model is developed for a nuclear rocket. The resultant equations for the optimal control problem are a pair of coupled, bilinear, partial differential equations. The thermal stress constraint forms an inequality which is a function of both the state and the control. The initial conditions are steady state, and the terminal condition is that the coolant flow obtain a fixed, higher level. The distributed parameter system is discretized in the space dimension to give an arbitrary order set of ordinary differential, state equations. It is shown how a result based on the Weierstrass necessary condition and derived by Berkovitz from the calculus of variations using a slack variable technique may be applied. This condition is shown to require the optimal control to be “boundary control” with no switching. The optimal control program must make the inequality constraint an equality at some location throughout the transient. Based on the result that boundary control is the optimal control, an algorithm is developed to compute the optimal control program. The algorithm was programmed on a digital computer and numerical results are given for the optimal flow program and the resultant stress distributions for various cases.

Three Turnaround Heat Treating Studies

2003 ◽  
Author(s):  
Jaan Taagepera ◽  
Marty Clift ◽  
D. Mike DeHart ◽  
Keneth Marden
Keyword(s):  
Heat Treatment ◽  
Finite Element Analysis ◽  
Finite Element ◽  
Thermal Stress ◽  
Thermal Stresses ◽  
Heat Treating ◽  
Element Analysis ◽  
Stress Profiles ◽  
Insight Into

Three vessel modifications requiring heat treatment were analyzed prior to and during a planned turnaround at a refinery. One was a thick nozzle that required weld build up. This nozzle had been in hydrogen service and required bake-out to reduce the potential for cracking during the weld build up. Finite element analysis was used to study the thermal stresses involved in the bake-out. Another heat treatment studied was a PWHT of a nozzle replacement. The heat treatment band and temperature were varied with location in order to minimize cost and reduction in remaining strength of the vessel. Again, FEA was used to provide insight into the thermal stress profiles during heat treatment. The fmal heat treatment study was for inserting a new nozzle in a 1-1/4Cr-1/2Mo reactor. While this material would ordinarily require PWHT, the alteration was proposed to be installed without PWHT. Though accepted by the Jurisdiction, this nozzle installation was ultimately cancelled.

Steady-State Thermal Stresses in Wedge-Shaped Cutting Tools

1975 ◽  
Vol 97 (3) ◽  
pp. 1060-1066
Author(s):  
P. F. Thomason
Keyword(s):  
Thermal Stress ◽  
Steady State ◽  
Metal Cutting ◽  
Thermal Stresses ◽  
Heat Conduction Problem ◽  
Equivalent Stress ◽  
Cutting Tools ◽  
Thermoelastic Stress ◽  
Plastic State ◽  
Steady State Heat

Closed form expressions for the steady-state thermal stresses in a π/2 wedge, subject to constant-temperature heat sources on the rake and flank contact segments, are obtained from a conformal mapping solution to the steady-state heat conduction problem. It is shown, following a theorem of Muskhelishvili, that the only nonzero thermal stress in the plane-strain wedge is that acting normal to the wedge plane. The thermal stress solutions are superimposed on a previously published isothermal cutting-load solution, to give the complete thermoelastic stress distribution at the wedge surfaces. The thermoelastic stresses are then used to determine the distribution of the equivalent stress, and this gives an indication of the regions on a cutting tool which are likely to be in the plastic state. The results are discussed in relation to the problems of flank wear and rakeface crater wear in metal cutting tools.

Modelling of Convective Melt Flow and Interface Shape in Commercial Bridgman-Stockbarger Growth of CdZnTe

2000 ◽  
Author(s):  
Toby D. Rule ◽  
Ben Q. Li ◽  
Kelvin G. Lynn
Keyword(s):  
Heat Transfer ◽  
Thermal Stress ◽  
Solute Transport ◽  
Latent Heat ◽  
Thermal Stresses ◽  
Radiation Detector ◽  
Time History ◽  
High Quality ◽  
Melt Convection ◽  
The Impact

Abstract CdZnTe single crystals for radiation detector and IR substrate applications must be of high quality and controlled purity. The growth of such crystals from a melt is very difficult due to the low thermal conductivity and high latent heat of the material, and the ease with which dislocations, twins and precipitates are introduced during crystal growth. These defects may be related to solute transport phenomena and thermal stresses associated with the solidification process. As a result, production of high quality material requires excellent thermal control during the entire growth process. A comprehensive model is being developed to account for radiation and conduction within the furnace, thermal coupling between the furnace and growth crucible, and finally the thermal stress fields within the growing crystal which result from the thermal conditions imposed on the crucible. As part of this effort, the present work examines the heat transfer and fluid flow within the crucible, using thermal boundary conditions obtained from experimental measurements. The 2-D axisymetric numerical model uses the deforming finite element method, with allowance made for melt convection, solidification with latent heat release and conjugate heat transfer between the solid material and the melt. Results are presented for several stages of growth, including a time-history of the solid-liquid interface (1365 K isotherm). The impact of melt convection, thermal end conditions and furnace temperature gradient on the growth interface is evaluated. Future work will extend the present model to include radiation exchange within the furnace, and a transient analysis for studying solute transport and thermal stress.

scholarly journals Measurement and Isolation of Thermal Stress in Silicon-On-Glass MEMS Structures

Sensors ◽  
2018 ◽  
Vol 18 (8) ◽  
pp. 2603 ◽  
Author(s):  
Zhiyong Chen ◽  
Meifeng Guo ◽  
Rong Zhang ◽  
Bin Zhou ◽  
Qi Wei
Keyword(s):  
Thermal Stress ◽  
Natural Frequency ◽  
Frequency Conversion ◽  
Thermal Stresses ◽  
Sensors And Actuators ◽  
Stress Variation ◽  
Rigid Frame ◽  
Measured Stress ◽  
Stress Isolation ◽  
Frequency Variations

The mechanical stress in silicon-on-glass MEMS structures and a stress isolation scheme were studied by analysis and experimentation. Double-ended tuning forks (DETFs) were used to measure the stress based on the stress-frequency conversion effect. Considering the coefficients of thermal expansion (CTEs) of silicon and glass and the temperature coefficient of the Young’s modulus of silicon, the sensitivity of the natural frequency to temperature change was analyzed. A stress isolation mechanism composed of annular isolators and a rigid frame is proposed to prevent the structure inside the frame from being subjected to thermal stresses. DETFs without and with one- or two-stage isolation frames with the orientations <110> and <100> were designed, the stress and natural frequency variations with temperature were simulated and measured. The experimental results show that in the temperature range of −50 °C to 85 °C, the stress varied from −18 MPa to 10 MPa in the orientation <110> and −11 MPa to 5 MPa in the orientation <100>. For the 1-stage isolated DETF of <110> orientation, the measured stress variation was only 0.082 MPa. The thermal stress can be mostly rejected by a stress isolation structure, which is applicable in the design of stress-sensitive MEMS sensors and actuators.

Numerical Study of Thermal Stresses in a Planar Solid Oxide Fuel Cell Stack

2017 ◽  
Author(s):  
Cun Wang ◽  
Tao Zhang ◽  
Cheng Zhao ◽  
Jian Pu
Keyword(s):  
Thermal Stress ◽  
Fuel Cell ◽  
Solid Oxide Fuel Cell ◽  
Thermal Stresses ◽  
Coefficient Of Thermal Expansion ◽  
Numerical Study ◽  
Solid Oxide ◽  
Oxide Fuel ◽  
Compressive Loads ◽  
Cte Mismatch

A three dimensional numerical model of a practical planar solid oxide fuel cell (SOFC) stack based on the finite element method is constructed to analyze the thermal stress generated at different uniform temperatures. Effects of cell positions, different compressive loads, and coefficient of thermal expansion (CTE) mismatch of different SOFC components on the thermal stress distribution are investigated in this work. Numerical results indicate that the maximum thermal stress appears at the corner of the interface between ceramic sealants and cells. Meanwhile the maximum thermal stress at high temperature is significantly larger than that at room temperature (RT) and presents linear growth with the increase of operating temperature. Since the SOFC stack is under the combined action of mechanical and thermal loads, the distribution of thermal stress in the components such as interconnects and ceramic sealants are greatly controlled by the CTE mismatch and scarcely influenced by the compressive loads.

scholarly journals Numerical Simulation Study on the Front Shape and Thermal Stresses in Growing Multicrystalline Silicon Ingot: Process and Structural Design

Crystals ◽  
2020 ◽  
Vol 10 (11) ◽  
pp. 1053
Author(s):  
Chengmin Chen ◽  
Guangxia Liu ◽  
Lei Zhang ◽  
Guodong Wang ◽  
Yanjin Hou ◽  
...  
Keyword(s):  
Numerical Simulation ◽  
Thermal Stress ◽  
Thermal Stresses ◽  
Simulation Method ◽  
Power Ratio ◽  
Radial Temperature ◽  
Front Shape ◽  
Simulation Results ◽  
Insulation Block ◽  
Transient Numerical Simulation

In this paper, a transient numerical simulation method is used to investigate the effects of the two furnace configurations on the thermal field: the shape of the melt–crystal (M/C) interface and the thermal stress in the growing multicrystalline ingot. First, four different power ratios (top power to side power) are investigated, and then three positions (i.e., the vertical, angled, and horizontal positions) of the insulation block are compared with the conventional setup. The power ratio simulation results show that with a descending power ratio, the M/C interface becomes flatter and the thermal stress in the solidified ingot is lower. In our cases, a power ratio of 1:3–1:4 is more feasible for high-quality ingot. The block’s position simulation results indicate that the horizontal block can more effectively reduce the radial temperature gradient, resulting in a flatter M/C interface and lower thermal stress.

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